I wish to test some model fitting software and I would like to generate synthetic datasets for this test. The synthetic data is supposed to originate from a experiment that measures the change in concentration of a substance over time. I can generate error free data for such an experiment using a differential equation model. My question however is what kind of noise should I add so that the data resembles a real experimental dataset? My current two choices are to either add noise from a gaussian or exponential distribution, any preferences? (Eg adding gaussian noise could potentially generate negative concentrations)
My other concern is should the degree of noise be equal for all data points? For example I would imagine there would be more uncertainty in small concentrations that larger ones, simply because it is more difficult to measure small concentrations.